If \(\lbrace \Lambda _j\rbrace _{j\in J}\)  is a g-frame for \(H\)  with bounds \(A\)  and \(B\) , respectively, then \(\lbrace \tilde{\Lambda }_j\rbrace _{j\in J}\)  is a g-frame for \(H\)  too with bounds \(B^{-1}\)  and \(A^{-1}\) , respectively (for more details, see [1]}).
